The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011–2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-M split estimation, which allows to estimate a vector of parameter differences and the Shift- M split (+) that is a generalisation of Shift- M split estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2 nd , 3 rd and 4 th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.
The summary of research activities concerning general theory and methodology performed in Poland in the period of 2015–2018 is presented as a national report for the 27th IUGG (International Union of Geodesy and Geophysics) General Assembly. It contains the results of research on new or improved methods and variants of robust parameter estimation and their application, especially to control network analysis. Reliability analysis of the observation system and an integrated adjustment approach are also given. The identifiability (ID) index as a new measure for minimal detectable bias (MDB) in the observation system of a network, has been introduced. A new method of covariance function parameter estimation in the least squares collocation has been developed. The robustified version of the Shift-Msplit estimation, termed as Shift-M*split estimation, which enables estimation of parameter differences (robustly), without the need of prior estimation of the parameters, has been introduced. Results on the analysis of geodetic time series, particularly Earth orientation parameter time series, geocenter time series, permanent station coordinates and sea level variation time series are also provided in this review paper. The entire bibliography of related works is provided in the references.
This paper presents the summary of research activities carried out in Poland in 2011–2014 in the field of Earth rotation and geodynamics by several Polish research institutions. It contains a summary of works on Earth rotation, including evaluation and prediction of its parameters and analysis of the related excitation data as well as research on associated geodynamic phenomena such as geocentre motion, global sea level change and hydrological processes. The second part of the paper deals with monitoring of geodynamic phenomena. It contains analysis of geodynamic networks of local, and regional scale using space (GNSS and SLR) techniques, Earth tides monitoring with gravimeters and water-tube hydrostatic clinometer, and the determination of secular variation of the Earth’ magnetic field.